Trajectory of a Spacecraft When It Passes by a Gravitational Body During Interstellar Travel

Interstellar space missions will require spacecraft that travel at relativistic speeds. Furthermore, their trajectories will be influenced by gravitational sources. Accordingly, this paper applies to interstellar missions a recently developed formulation of relativistic mechanics that predicts a spacecraft's trajectory when it passes by a gravitational source at a relativistic speed. The formulation, called spacetime impetus, is unique in that it employs a relativistic universal law of gravitation that does not explicitly require general relativity while producing precisely the same results. Based on these developments, an analyst can now update nonrelativistic mission planning codes to give them general relativistic capabilities. It requires augmenting the code with relativistic velocities and relativistic accelerations, the replacement of the universal law of gravitation with a relativistic universal law of gravitation, and setting up Lorentz transformations between frames.